Today we seemed to be confused on how to fill in the table that was for homework. The first equation we did looked at was:

**f(x) = x**

^{2}+ 5x + 6.The first thing we would do with this is

__factor__the equation..

**f(x) = (x-2)(x-3)**

Now that we've factored the equation, we're able to pin-point the

__roots/ y-intercepts/ zeros__.

**2, 3**

******Don't forget to switch the signs (-, +)!

__REMINDER__:*Negative (-) to positive (+) and vice versa.*

Okay, so we have our roots and having the roots we can easily find the

__Axis of Symmetry__.

**Step 1:**Add both roots together.

**2 + 3 = 5**

**Step 2:**Now that we have the sum of the two roots, we divide by 2 to find the center of the roots which is the

__Axis of Symmetry__.

**5 / 2**

**NOTE:**It's a lot easier to work with fractions than decimals!

So the answer to what the

__Axis of Symmetry__is:

**x = 5 / 2**

******Don't forget to put x = before the numbers!

__REMINDER__:Now that we've found the

__Axis of Symmetry__(which is

**also**the x-coordinate of the vertex) we're able to plug that number into the equation

**f(x) = (x-2)(x-3)**to find the

__max or min__value(which is

**also**the y-coordinate of the vertex). This is how:

**f(5/2) = (5/2 - 2)(5/2 - 3)**

**f(5/2) = (5/2 - 4/2)(5/2 - 6/2)**

Lets stop right there just in case anyone doesn't understand how we went from

**- 2**to

**- 4/2**and from

**- 3**to

**- 6/2**. Well going back to grade nine or so, we should know that when adding fractions the denominators have to be the same. And knowing that whatever we do with the bottom we must do to the top, we multiply the bottom (1) by

**2**to be the same as

**5/2**and then multiply the top (2) by 2 as well. The result is

**4/2**. We do the same for the

**- 3**.

Continuing...Continuing...

**f(5/2) = (1/2)(-1/2)**

**f(5/2) = - 1/4**

Your answer should look like this:Your answer should look like this:

**min y = - 1/4**

And there you go, you've got your

__max or min__value.

Okay! So lets recap.

Okay! So lets recap.

- By factoring the equation we found the

__roots__.**2, 3**- and with the roots we easily found the

__Axis of Symmetry__.**5/2**- Knowing that the

__Axis of Symmetry__is the x-coordinate of the__vertex__, we found half of the__vertex__**. ( 5/2, ___)**- Plugging the

__Axis of Symmetry__into the equation we found the__max or min__value which we also know is the same as the y-coordinate of the__vertex__.**( 5/2, -1/4 )**We're not finished yet, though. The easiest way to figure out if the

__parabola__opens up or down is to look at the the sign (-, +) in front of the equation itself. Looking back at the original equation there was a

**+**sign:

**f(x) = x**

^{2}- 5x + 6

The answer for whether this equation opens up or down is:The answer for whether this equation opens up or down is:

**UP.**

As for domain, everyone should know that. Like Mr. K says,

**"It's a gimme!"**

With these particular

__parabolas__, the domain with always be:

**D: (- oo, oo)**

The range (y-axis) is, just like the domain, smaller number, comma, then the larger number. This

__parabolas__smallest number is the

__max or min__value. If the number is a max value, the number goes where the "larger number" is placed -- after the comma. If the number is a min value, the number goes where the "smaller number" is placed -- before the comma. In this case, we have a min value so the range should look like this:

**R: [-1/4, oo)**

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The second thing thing we went over was question 2 on the worksheet. It looked like this:

**Find the equation of the quadratic function given its vertex is (1, -2) and a point on the graph at (-2, 16).**

The first thing we should do is find the easiest equation to put this information into. This happens to be this:

**y = a(x-h)**

^{2}+ kWe know the vertex so we can easily put those numbers into the equation so it looks like this:

**y = a(x-1)**

^{2}- 2We also know a point on the graph which are the x and y coordinates! Those fit into the equation as well like so:

**16 = a(-2 -1)**

^{2}- 2Now all we have to do is solve for

**a**!!

**16 = a(-2 -1)**

^{2}- 2**16 = a(-3)**

^{2}- 2**16 = a(9) - 2**

**16 = 9a - 2**

**16 + 2 = 9a**

**18 = 9a**

**18/9 = 9a/9**

**2 = a**

Now that you have

**a,**you can now

**find the equation for the quadratic function**.

**y = 2(-2 -1)**

^{2}- 2Alright! I think i've covered everything and there you have it. With the simplest information you can find EVERYTHING you need. Great hey? (=

Today's homework is:

1.) Sign up for the websites that Mr. K posted up.

2.) Exercise 6!

Have fun guys!

ANNDD..

ANNDD..

**Last but not least, tomorrows scribe will be...**

.

.

.

.

.

.

**melissa!!**

Have fun! =)

Yay, Sandy!! Aw, you sounded grrrrrrreat. I think better than I did? I honestly didn't think my scribe was applause worthy, but thanks, guys! Good job on your scribe dandy Sandy. K i dunno. Byeee!

ReplyDeleteQUOTE:

ReplyDelete"By the way Cherrie, great job on your scribe! As for myself, I hope I can do just as good."

It looks like there could be some competition going on here...

exactly...theres compitition!

ReplyDeletegood job!

..

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Hi Sandy,

ReplyDeleteWhat a great scribe! I felt as if you were right here talking to me--

The underlines, and the reminders and notes were very helpful.

Best,

Lani